reply to Mizrach's reply

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There is an interesting issue about teaching that Mizrach points up when he
substitutes "cutting through the B.S." for the "naieve question." The
implication that the teacher's attempt to make clear his analytical framework
is B. S. is a common response of students to the traffic in abstractions.
I won't belabor the necessity of dealing with various orders of abstraction
in order to create a framework for understanding patterning of any sort. The
trick for a writer and a teacher is keeping the logical levels straight and
connecting them clearly to the data to be explained. If this is done with
care--which means making every possible concession to the reader/listener--
then the student will not only follow the argument, but will often jump to a
conclusion. The commonest conclusions students jump to, in my experience, is
the specific application of the framework being developed. This results in
the most common type of question, which is usually a specific case or a
specific kind of case to which the framework applies. This is one kind of
naive question, but there are others. What they ordinarily have in common is
that the logical level of the question is usually less abstract than the
framework the teacher was developing. This is the flashpoint in any class.

The question usually interrupts the line of reasoning and/or the train of
thought the teacher was developing. A common response of teachers is to
ignore or brush off the question in order to continue the train of argument
to the end. This is most often (but not always) a big mistake for one of two
reasons. If the student's question logically follows from the argument, then
its implication is patent--if the teacher hears it. If it logically follows,
and the implication is not one that the teacher had in mind, then the frame-
work being developed is more powerful than the teacher understood at the
outset. If the question seems not to follow from the line of argument, it may
be because there is a problem with the presentation or a problem withe the
argument. In either case, this is something the teacher needs to know. There
is a technique for handling these questions that a colleague taught me years
ago. You have to stop dead where you are in the argument, press the clear
button, and listen to the question _as asked_. If you're not sure where the
student is coming from, then you have to ask the student to clarify his/her
question/statement. If you do understand the question, it is still a good
idea to ask the student to clarify. This is how you identify the holes in
your argument, the ambiguities in your presentation, or, heaven forbid, your
logical errors. Then you have to answer the question at the level at which it
is asked and use the answer to work back to where you stopped. This forces
you to keep the levels of abstraction straight and to work top-down AND
bottom up. If you've developed a clear line of argument, then you should
expect that any intelligent student will be able to see where it is going and
come up with empirical (or hypothetical) cases that either illustrate it or
contradict it. You can also expect your more pompous students, having
figured out the line of argument and jumped to the end, to claim to have cut
through the B. S.. That goes with the territory.

Mike Lieber

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